Solve (3x^{2})^{3}*(-4y^3)^2div(6x^2y)^6

$$( 3 x ^ { 2 } ) ^ { 3 } \cdot ( - 4 y ^ { 3 } ) ^ { 2 } \div ( 6 x ^ { 2 } y ) ^ { 6 }$$

Evaluate

$$\frac{1}{108x^{6}}$$

Solution Steps

Expand \left(3x^{2}\right)^{3}.

$$\frac{3^{3}\left(x^{2}\right)^{3}\left(-4y^{3}\right)^{2}}{\left(6x^{2}y\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{3^{3}x^{6}\left(-4y^{3}\right)^{2}}{\left(6x^{2}y\right)^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27x^{6}\left(-4y^{3}\right)^{2}}{\left(6x^{2}y\right)^{6}}$$

Expand \left(-4y^{3}\right)^{2}.

$$\frac{27x^{6}\left(-4\right)^{2}\left(y^{3}\right)^{2}}{\left(6x^{2}y\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{27x^{6}\left(-4\right)^{2}y^{6}}{\left(6x^{2}y\right)^{6}}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{27x^{6}\times 16y^{6}}{\left(6x^{2}y\right)^{6}}$$

Multiply 27 and 16 to get 432.

$$\frac{432x^{6}y^{6}}{\left(6x^{2}y\right)^{6}}$$

Expand \left(6x^{2}y\right)^{6}.

$$\frac{432x^{6}y^{6}}{6^{6}\left(x^{2}\right)^{6}y^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{432x^{6}y^{6}}{6^{6}x^{12}y^{6}}$$

Calculate 6 to the power of 6 and get 46656.

$$\frac{432x^{6}y^{6}}{46656x^{12}y^{6}}$$

Cancel out 432x^{6}y^{6} in both numerator and denominator.

$$\frac{1}{108x^{6}}$$

Expand

$$\frac{1}{108x^{6}}$$

Solution Steps

Expand \left(3x^{2}\right)^{3}.

$$\frac{3^{3}\left(x^{2}\right)^{3}\left(-4y^{3}\right)^{2}}{\left(6x^{2}y\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{3^{3}x^{6}\left(-4y^{3}\right)^{2}}{\left(6x^{2}y\right)^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27x^{6}\left(-4y^{3}\right)^{2}}{\left(6x^{2}y\right)^{6}}$$

Expand \left(-4y^{3}\right)^{2}.

$$\frac{27x^{6}\left(-4\right)^{2}\left(y^{3}\right)^{2}}{\left(6x^{2}y\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{27x^{6}\left(-4\right)^{2}y^{6}}{\left(6x^{2}y\right)^{6}}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{27x^{6}\times 16y^{6}}{\left(6x^{2}y\right)^{6}}$$

Multiply 27 and 16 to get 432.

$$\frac{432x^{6}y^{6}}{\left(6x^{2}y\right)^{6}}$$

Expand \left(6x^{2}y\right)^{6}.

$$\frac{432x^{6}y^{6}}{6^{6}\left(x^{2}\right)^{6}y^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{432x^{6}y^{6}}{6^{6}x^{12}y^{6}}$$

Calculate 6 to the power of 6 and get 46656.

$$\frac{432x^{6}y^{6}}{46656x^{12}y^{6}}$$

Cancel out 432x^{6}y^{6} in both numerator and denominator.

$$\frac{1}{108x^{6}}$$